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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=-21/4, b>=a > For fixed z and a=-21/4, b=-13/4





http://functions.wolfram.com/07.23.03.a89k.01









  


  










Input Form





Hypergeometric2F1[-(21/4), -(13/4), 9/2, z] == (1/(406156115673 Pi^(3/2) z^(7/2))) (4 (-2 Sqrt[z] (-172380 + 4007835 z - 59005674 z^2 - 24113491899 z^3 - 85011359916 z^4 - 67561161675 z^5 - 12136704314 z^6 - 102922677 z^7 + 2249676 z^8) EllipticE[(1/2) (1 - Sqrt[z])] - 2 Sqrt[z] (-172380 + 4007835 z - 59005674 z^2 - 24113491899 z^3 - 85011359916 z^4 - 67561161675 z^5 - 12136704314 z^6 - 102922677 z^7 + 2249676 z^8) EllipticE[(1/2) (1 + Sqrt[z])] + (344760 - 172380 Sqrt[z] - 8274240 z + 4007835 z^(3/2) + 123984315 z^2 - 59005674 z^(5/2) - 2630156802 z^3 - 24113491899 z^(7/2) - 39622863483 z^4 - 85011359916 z^(9/2) - 88461734172 z^5 - 67561161675 z^(11/2) - 51547032971 z^6 - 12136704314 z^(13/2) - 6833390850 z^7 - 102922677 z^(15/2) + 562419 z^8 + 2249676 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (-344760 - 172380 Sqrt[z] + 8274240 z + 4007835 z^(3/2) - 123984315 z^2 - 59005674 z^(5/2) + 2630156802 z^3 - 24113491899 z^(7/2) + 39622863483 z^4 - 85011359916 z^(9/2) + 88461734172 z^5 - 67561161675 z^(11/2) + 51547032971 z^6 - 12136704314 z^(13/2) + 6833390850 z^7 - 102922677 z^(15/2) - 562419 z^8 + 2249676 z^(17/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[1/4]^2)










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02